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Physical review. B, Condensed matter

Dynamic critical exponents in Ising spin glasses

L. Bernardi, Ian A. Campbell

Published Jan 1, 1994• 18 citations
Publisher

Abstract

We have carried out dynamic simulations for Ising spin glasses on simple cubic lattices in dimension 3 with five different sets of near-neighbor interaction distributions. We find that the dynamic exponent in the power-law relaxation of the autocorrelation function at the ordering temperature varies considerably with the distribution chosen. This indicates that the standard universality rules do not appear to hold for these systems.

DOI
10.1103/physrevb.49.728

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We have carried out dynamic simulations for Ising spin glasses on simple cubic lattices in dimension 3 with five different sets of near-neighbor interaction distributions. We find that the dynamic exponent in the power-law relaxation of the autocorrelation function at the ordering temperature varies considerably with the distribution chosen. This indicates that the standard universality rules do not appear to hold for these systems.
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been carried out on Ising Spin Glasses in dimension three, using a technique where corrections to finite size scaling can be controled. The data show that the critical exponents vary strongly as a function of the kurtosis of the interaction distribution, a parameter which from the standard point of view should not be pertinent. This observation implies that for spin glasses the renormalization group analysis should not be approached in a the same way as in the case of canonical second order transitions; a much richer structure of universality classes would appear to exist for spin glasses.
We compare simulation data from different sources on two canonical three-dimensional Ising spin glasses (ISGs): the binomial $\ifmmode\pm\else\textpm\fi{}J$ near-neighbor interaction ISG and the Gaussian interaction ISG. We allow for the possibility of corrections to finite size scaling and estimate the correction exponent w. Consistent estimates for the critical temperatures Tg{T}_{g}Tg​ and for the critical exponents for each system are obtained. The data strongly indicate that critical exponents in the two systems are significantly different from each other. These results thus confirm a breakdown of standard universality rules in Ising spin glasses.
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately established using a standard criterion, critical exponents and correction terms can be readily estimated by extrapolating measurements made in the thermodynamic limit regime. The data show that the critical exponents of the susceptibility γγγ and of the correlation length ννν depend on the form of the interaction distribution. This observation implies that quite generally critical exponents are not universal in ISGs.
The critical dynamics of Ising spin glasses with bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent zc{z}_{c}zc​, the nonequilibrium autocorrelation decay exponent ${\ensuremath{\lambda}}_{c}∕{z}_{\mathrm{c}}$, and the critical fluctuation-dissipation ratio ${X}_{\ensuremath{\infty}}$ all vary strongly and systematically with the form of the interaction distribution.